As far as I can tell, there is no major critic who specializes in explaining what playing a given game feels like, nor is anyone analyzing what specific games mean in any context outside the game itself.My first reaction to this quote was, "But I do know what playing games feels like." However, as far as I know no critic, myself included, effectively communicates this in their pieces. Let me show you what I mean.
Here's a clip of two people playing a match of Super Smash Bros. Melee. Watch the whole thing if you like, but the part most relevant to what I'm going to talk about begins at 1:05.
If you're a regular Smash Bros. player, your reaction to the video will likely be vastly different from someone who has never played before or played only a little bit. If you're a regular player, you know why Marth falling through the level -- twice -- is out of the ordinary. You might even find it funny, as I sure did.
Now, try to communicate that to someone who has never played before. Before you can explain why it's funny, you would have to explain the basics of the game, how recovery works, who the characters are, what the stage is, and so on. You have to explain a lot. And after you've explained all that, the non-player still probably won't find the clip funny. We all know the old adage about how a joke isn't funny if you have to explain it.
And so we've reached the dilemma. As someone who's familiar with Smash Bros., I know what it feels like to experience something like what happens in that clip. I know how intense a well-played Smash Bros. match feels. I know the thrill of victory, the agony of defeat, and how hilarious it is when something completely unexpected happens, such as in the above clip. In fact, I'd argue that the random unexpected occurrences are what make Smash Bros. so great.
But if you're writing to someone who's never played the game before, how the hell are you supposed to communicate all of that effectively? Unless your audience is already familiar with at least some vital aspects of the game, I don't see how it's possible.
Fortunately, I think this will become easier as games become a more indelible part of popular culture. As more people play games, the more familiar they become with genres, tropes and common features. Most people already know who Mario is, and he appears in Super Smash Bros. Melee, so you wouldn't have to explain who he is if you were writing about that game. My hope is that, over time, you won't have to explain things like "platform" or "recovery" either, because they will be as identifiable as Mario.